rTPC (version 1.0.4)

quadratic_2008: Quadratic model for fitting thermal performance curves

Description

Quadratic model for fitting thermal performance curves

Usage

quadratic_2008(temp, a, b, c)

Value

a numeric vector of rate values based on the temperatures and parameter values provided to the function

Arguments

temp

temperature in degrees centigrade

a

parameter that defines the rate at 0 ºC

b

parameter with no biological meaning

c

parameter with no biological meaning

Details

Equation: $$rate = a + b \cdot temp + c \cdot temp^2$$

Start values in get_start_vals are derived from the data using previous methods in the literature

Limits in get_lower_lims and get_upper_lims are based on extreme values that are unlikely to occur in ecological settings.

References

Montagnes, David JS, et al. Short‐term temperature change may impact freshwater carbon flux: a microbial perspective. Global Change Biology 14.12: 2823-2838. (2008)

Examples

# load in ggplot
library(ggplot2)

# subset for the first TPC curve
data('chlorella_tpc')
d <- subset(chlorella_tpc, curve_id == 1)

# get start values and fit model
start_vals <- get_start_vals(d$temp, d$rate, model_name = 'quadratic_2008')
# fit model
mod <- nls.multstart::nls_multstart(rate~quadratic_2008(temp = temp, a, b, c),
data = d,
iter = c(4,4,4),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'quadratic_2008'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'quadratic_2008'),
supp_errors = 'Y',
convergence_count = FALSE)

# look at model fit
summary(mod)

# get predictions
preds <- data.frame(temp = seq(min(d$temp), max(d$temp), length.out = 100))
preds <- broom::augment(mod, newdata = preds)

# plot
ggplot(preds) +
geom_point(aes(temp, rate), d) +
geom_line(aes(temp, .fitted), col = 'blue') +
theme_bw()